THE FOLD / SPAWN / CHECKPOINT ZERO / THE CHOMP
THE CHOMP
a win with no strategy attached
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Chomp: a rectangle of squares, the bottom-left one poisoned. Take any square and everything above and to the right of it goes too. Eat the poison and you lose. Strategy stealing proves the first player wins on every board bigger than 1×1, and it does so without examining a single position: suppose biting the far corner left the opponent in a winning position — then the first player could simply have played that winning reply as his own opening. Either way a winning first move exists. The argument names none of them, and for general boards nobody knows what they are.
LIT verified live: solving every board from 2×2 to 4×4 by exhaustive game tree, the first player wins all 15 positions; the 1×1 board is the sole exception, where the only square is poison; and each tested board has a winning opening — 2×2, 3×3, 2×4 and 3×4 each with exactly 1 — while the move itself differs from board to board.
LIT verified live: solving every board from 2×2 to 4×4 by exhaustive game tree, the first player wins all 15 positions; the 1×1 board is the sole exception, where the only square is poison; and each tested board has a winning opening — 2×2, 3×3, 2×4 and 3×4 each with exactly 1 — while the move itself differs from board to board.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at CHECKPOINT ZERO, which is the poisoned square itself: the origin you must never return to, and the only square on the board that ends the game.
AVAN (AI) got the base case backwards and the sweep caught it. A first draft treated a position holding only the poison square as a win for the player to move — but that player has no legal move except eating it, so it is a loss. With taking the poison already excluded from the move list, the generic loop returns exactly that, and the explicit base case did nothing but invert it. The symptom was unmistakable: boards came back as second-player wins, contradicting a theorem that has stood since 1974. A wrong answer that contradicts something famous is the easy kind to catch; the reason to record it is that the same inversion in a less-known game would simply have been published.
AVAN (AI) got the base case backwards and the sweep caught it. A first draft treated a position holding only the poison square as a win for the player to move — but that player has no legal move except eating it, so it is a loss. With taking the poison already excluded from the move list, the generic loop returns exactly that, and the explicit base case did nothing but invert it. The symptom was unmistakable: boards came back as second-player wins, contradicting a theorem that has stood since 1974. A wrong answer that contradicts something famous is the easy kind to catch; the reason to record it is that the same inversion in a less-known game would simply have been published.
3 ONE DIMENSION
Every board solved. Every one a first-player win, and the theorem knew in advance.
4 TWO DIMENSIONS · INTERACTIVE
Take a bite and watch the verdict flip. The winning move is not where the proof points.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the game tree, with the winning openings lit and unexplained.
AVAN’s addition (the inverse-companion): the forward reading is “the first player wins.” The inverse is that the proof works by ruling out a possibility rather than by building anything, and that is why it hands over nothing. It never constructs a strategy, never inspects a board, never uses the rules of Chomp beyond the fact that a spare move can never hurt you. Read backwards, strategy stealing is a technique for converting ignorance about the opponent’s options into certainty about your own — and its power and its uselessness are the same property, because an argument that examined the position would have had to depend on it.
LIT solving every board from 2x2 to 4x4 by exhaustive game tree, the first player wins all 15 positions; the 1x1 board is the sole exception, where the only square is poison; and each tested board has a winning opening — 2x2, 3x3, 2x4 and 3x4 each with exactly 1 — while the move itself differs from board to board
FIG AVAN got the base case backwards and the sweep caught it. A first draft treated a position holding only the poison square as a WIN for the player to move, but that player has no legal move except eating it, so it is a LOSS. With poison-taking already excluded from the move list the generic loop returns exactly that, and the explicit base case did nothing but invert it. The symptom was unmistakable — boards came back as second-player wins, contradicting a theorem standing since 1974. The reason to record it is that the same inversion in a less-known game would simply have been published.
FIG AVAN got the base case backwards and the sweep caught it. A first draft treated a position holding only the poison square as a WIN for the player to move, but that player has no legal move except eating it, so it is a LOSS. With poison-taking already excluded from the move list the generic loop returns exactly that, and the explicit base case did nothing but invert it. The symptom was unmistakable — boards came back as second-player wins, contradicting a theorem standing since 1974. The reason to record it is that the same inversion in a less-known game would simply have been published.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of CHECKPOINT ZERO · David Lee Wise (ROOT0), with AVAN